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On the mixing of angular momentum in a stirred rotating fluid

  • F. P. Bretherton (a1) and J. S. Turner (a1)

Abstract

It has been suggested on theoretical grounds that a vortex could be initiated in a cylindrical region of fluid, originally in solid rotation, by the horizontal mixing of angular momentum produced by external stirring. In this paper various arguments for and against the mechanism are examined and their difficulties exposed. No firm conclusion is reached. A series of mathematical models of the mixing motions has been used, to bring out the differences between mechanical stirring and the agitation of a gas by random molecular motions. They suggest the introduction of a diffusion coefficient for angular momentum, to be determined empirically. These theoretical ideas are then applied to the interpretation of the results of a laboratory experiment which has been designed to test the proposed mechanism directly.

A wide, flat tank of liquid was set up on a rotating table and stirred with a vertically oscillated grid, whose elements were much smaller than the width of the tank. A neutrally buoyant particle was used as a tracer of fluid motions, to measure relative circulation velocities and the properties of the turbulence. The motion observed was dominated by the loss of angular momentum to the walls and the grid, an effect which has not been taken into account in previous theoretical assessments of the effects of mixing of angular momentum. The relative circulation present was not significantly different from zero, and the limits of error of the measurements imply that the rate of diffusion of angular momentum is less than 5% of that for fluid particles, with 95% probability.

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References

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Batchelor, G. K. 1967 Introduction to Fluid Dynamics. Cambridge University Press.
Gough, D. O. & LYNDEN-BELL, D. 1968 J. Fluid Mech. 32, 437.
Kippenhahn, R. 1963 Astrophys J. 137, 664678.
KÜCHEMANN, D. 1965 J. Fluid Mech. 21, 120.
Prandtl, L. 1931 Proceedings of the World Engineering Congress, Tokyo, 5, 495507.
Rayleigh, LORD 1916 Scientific Papers, 6, 447.
Scorer, R. S. 1965 Report entitled: Vorticity in Nature, Department of Mathematics, Imperial College, London.
Scorer, R. S. 1966 Sci. J. 2, 4652.
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On the mixing of angular momentum in a stirred rotating fluid

  • F. P. Bretherton (a1) and J. S. Turner (a1)

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